The vacuum Robinson–Trautman solution admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. We perform a comprehensive classification of solutions exhibiting this property in Einstein’s gravity with a massless scalar field, assuming that the solution belongs at least to Petrov-type II and some of the components of Ricci tensor identically vanish. We find that these solutions can be grouped into three distinct classes: (I-a) a natural extension of the Robinson–Trautman family incorporating a scalar hair satisfying the time derivative of the Ricci flow equation, (I-b) a novel non-asymptotically flat solution characterized by two functions satisfying Perelman’s pair of the Ricci flow equations, and (II) a dynamical solution possessing SO(3) , ISO(2) or SO(1,2) symmetry. We provide a complete list of all explicit solutions falling into Petrov type D for classes (I-a) and (I-b). Moreover, leveraging the massless solution in class (I-a), we derive the neutral Robinson–Trautman solution to the N=2 gauged supergravity with the prepotential F(X)=−iX0X1 . By flipping the sign of the kinetic term of the scalar field, the Petrov-D class (I-a) solution leads to a time-dependent wormhole with an instantaneous spacetime singularity. Although the general solution is unavailable for class (II), we find a new dynamical solution with spherical symmetry from the anti-de Sitter (AdS)–Roberts solution via AdS/Ricci-flat correspondence.

中文翻译：

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具有标量毛发和 Ricci 流的 Robinson-Trautman 解

真空 Robinson-Trautman 解允许无剪切、无扭曲的零测地线同余和非零展开。我们对在无质量标量场的爱因斯坦引力中表现出这种性质的解进行了全面的分类，假设该解至少属于 Petrov-II 型并且 Ricci 张量的一些分量同样消失。我们发现这些解可以分为三个不同的类别：（Ia）罗宾逊-特劳特曼族的自然延伸，包含满足里奇流方程时间导数的标量头发，（Ib）一种新颖的非渐近平坦解，其特征在于由满足佩雷尔曼的里奇流方程对的两个函数，以及 (II) 具有的动态解 所以（3） , 国际标准化组织（2） 或者 所以（1,2） 对称。我们提供了 (Ia) 和 (Ib) 类属于 Petrov D 型的所有显式解的完整列表。此外，利用 (Ia) 类中的无质量解，我们推导了中性 Robinson-Trautman 解 氮=2 用预势测量超重力 F（X）=-我X0X1 。通过翻转标量场动力学项的符号，Petrov-D 类 (Ia) 解产生了具有瞬时时空奇点的时间相关虫洞。尽管一般解对于 (II) 类不可用，但我们通过 AdS/Ricci 平坦对应关系从反德西特 (AdS)-Roberts 解中找到了一种具有球对称性的新动力学解。